4 EXPOSED PENSTOCKS This section discusses the parameters to be considered in the design and analysis of exposed penstocks. 4.1 Penstock Shell Design and Analysis The principal factors that govern the required shell thickness are: (1) Thickness required for shipment and handling (2) Thickness required to resist the imposed loads, considering the appropriate allowable stresses. Additional factors in determining shell thickness include: (1) Acceptance criteria for mill and fabrication tolerances (2) Criteria for corrosion allowance, if elected in lieu of coating and lining. LU 73 l 4 Exposed Penstocks 4.1.1 Minimum Shell Thickness The minimum thickness of the penstock shell should be the larger of the following thickness values: (1) Thickness required to ensure adequate shipment and handling, as required by this manual. (2) Thickness required to resist the imposed loads, given certain allowable stress conditions and considering that the shell thickness is to be specified within recommended mill and fabrication tolerances. The possible allowance for corrosion must be considered as an addition to the required thickness for design. (3) In addition to minimum shell thickness for handling, the shell thickness, support types, and support spacing must be selected so that the maximum deflection of the pipe filled with water, acting as a beam between the supports, does not exceed 1/360 of the span. (4) Similarly, to avoid pipe buckling due to full internal vacuum, the Dit ratio should be not less than 158. If the ratio is less than 158, stiffeners may be required. 4.1.2 Determining Shell Thickness and Stresses Although the predominant stress-causing load on a penstock section (unrestrained and free from internal or external appurtenances) is the stress from internal pressure, it is important to recognize that other stress conditions can exist and should be considered in determining the required shell thickness. These additional stresses can result from beam action, differential temperatures, and longitudinal stress due to end closures free to move in a longitudinal direction. The stress (not hoop stress) caused directly by the internal pressure may be considered negligible. As such, and in the majority of cases, the stress analyses for determining the shell thickness ends as a biaxial state of stress and is resolved by application of either the Hencky-von Mises theory or the stress intensity approach discussed in Section 3.4. The following formulas can be used to determine shell thickness and stresses imposed by certain loading conditions. 4.1.2.1 Minimum Thickness for Shipping and Handling The minimum thickness (tm.,,) of the penstock shell for shipping and handling can be calculated using the formulas of Pacific Gas and Electric Company (PG&E) or the Bureau of Reclamation. This manual recommends use of the larger of the minimum thickness values calculated by the formulas. (1) PG&E formula D tmin = 074 rn 288 (Equation4-1) 4 Exposed Penstocks (2) Bureau of Reclamation formula D +20 &Mi -400 (Equation 4-2) Where: tmin D = minimum thickness, in. = nominal penstock diameter, in. The larger of the minimum thickness values calculated by the above formulas must be checked to determine ifthe shell can adequately support itself at a point load, as if it were resting on a flat surface and loaded by its own weight. The maximum stress (SmAx under this loading condition is given by: Smax -- 9Rt2W (Equation4-3) t Where: t W R = shell thickness, in. = unit weight of the shell material, lb/in.3 = radius of the middle surface of the pipe shell, in. Asmaller minimum thickness value, more in line with design thickness, is acceptable provided that bracing, special supports, or external stiffeners are used to accommodate handling, construction, or other conditions. Ifcorrosion allowance is considered in the design, the minimum thickness for shipping and handling must include the corrosion allowance. 4.1.2.2 Hoop Stress Due to Internal Pressure To determine hoop stress due to internal pressure, either of the following formulas may be used: Pr SE - Where: P t S Pr tE (Equation 4-4) (Equation 4-5) = internal pressure (at centerline of pipe), psi = penstock shell thickness required to resist the design pressure P, in. = basic allowable stress intensity for design load condition resulting in pressure P, psi LU 75 C 4 Exposed Penstocks SH = hoop stress due to internal pressure, psi r E = inside penstock radius, in. = weld joint reduction factor, in decimal percentage value Circumferential bending moments in a penstock shell occur whenever the penstock is partly filled. Shell design for a partly filled penstock has been treated in several articles, none of which gives a complete analysis. Good treatments of this complex analysis are given by R. J. Roark' and H. Schorer.2 Calculations using the formulas presented by Roark must be done with great precision because the expression for the bending moment represents the algebraic sum of large numbers of nearly equal terms. Circumferential bending moments for a completely filled penstock (zero pressure) exist only for a penstock supported on saddles. Depending on the saddle-to-shell configuration, formulas developed by L. P. Zick3 can be used. The shearing stresses developed in a transverse penstock section are due to the external loads, including weight of the shell and water. When the shell is held to a cylindrical shape by a stiffener ring, for example, the developed shear is tangent to the shell at all points and varies from zero at the top to zero at the bottom, with a maximum at mid-depth twice the average value over the entire section. When the shell is free to deform, as with a saddle support, the tangential shear stresses act on a reduced effective cross section, and the maximum stress occurs at the horn of the saddle. There is further increase in this shear stress because a portion of the shell above the saddle is noneffective, tending to increase the shear in the effective portion. 4.1.2.3 Longitudinal Stresses Longitudinal stresses are imposed on a penstock shell from several loading conditions. These stresses are generally categorized by the following action conditions: (1) beam action, (2) stiffener ring restraint at rim, (3) buckling due to axial compression, (4) radial strain (Poisson's effect), and (5) temperature-related effects. (1) Beam action When a penstock rests on its supports, it acts as a beam. The beam load consists of the weight of the pipe, the contained water, and any external live loads such as ice, snow, wind, or earthquake. Ifthe penstock is to function as a beam, deformation of the shell at the supports must be limited by the use of properly designed stiffener rings, ring girder supports, or saddle supports. On the assumption that large shell deformations can be prevented, the beam stresses can be computed using the theory of flexure. For a cylinder section, the resulting longitudinal stress intensity (SL) is given by: SL= MB IrCr2t Where: SL MB = = resulting longitudinal stress intensity, psi bending moment due to beam action, in.-lb cr) 0 Ml 76 (Equation4-6) 4 Exposed Penstocks r t = inside penstock radius, in. = nominal shell thickness, in. (2) Stiffener ring restraint Because of restraint imposed on the shell by a rigid ring girder or stiffener ring, secondary longitudinal bending stresses are developed in the pipe shell adjacent to the ring girder or stiffener ring. Although this is a local stress, which decreases rapidly with an increase in distance away from the ring, it should be considered in designing the plate for longitudinal stresses. These secondary stresses are flexural stresses caused by the bending deformation of the shell near the stiffener because the shell at the stiffener cannot widen radically in the same manner as the more distant shell portion. The maximum longitudinal bending stress (S#) is given by: SI1? (1.82) A - Ct (Pr) (Equation 4-7) Where: C = resulting longitudinal bending stress intensity due to ring girder action, psi = area of girder ring(s), plus shell area under and between rings, plus shell area to a distance on either side of the ring equal to 0.78 4-+, in a plane along the axis of the shell, in..2 = length of penstock shell measured between the out-to-out of girder rings, in. t = r P = inside penstock radius, in. = value of internal pressure at centerline of shell, psi S, Ar nominal shell thickness, in. To show the effect of the weight of water in the penstock, the weight of the penstock shell, and the joint reduction factor on the rim bending stresses, the factor PrIt in the above equation should be replaced by the hoop stress calculated for the shell. The recomputed SLB should be used in determining shell thickness. The longitudinal bending stress (Sw.x) in an axial direction, x distance from the ring girder edge, can be found by: SipRX = SiR(ýe)j ~-)jcos( 2+ Jt) (Equation 4-8) Where: SiR x = resulting longitudinal bending stress intensity due to ring girder action, psi = distance from the outside face of the girder ring at which point the ring restraining bending stress is being calculated, in. z is a constant for the cylindrical shell determined by: 7J 77 U 4 Exposed Penstocks ( - 4- (for steel with la = 0.303, z = 0.78 -1F+-) In current practice, if the maximum longitudinal restraining stresses are excessive, the shell thickness is increased on each side of the stiffener ring for a minimum length of LR = 2.33 \Frt. These secondary, longitudinal restraining stresses in the shell should be added algebraically to the longitudinal flexural stresses, if any, and the resultant used in shell thickness computations. The above formula for stresses due to ring girder action are for a penstock under pressure. A good treatment for calculating stress conditions with a half-full penstock is given by H. Schorer.2 Because it may control the design, this loading condition should be reviewed in combination with other applicable loads. Secondary, longitudinal restraining stresses for an unstiffened penstock supported on saddles are assumed to not exist. This assumption is based on the fact that the shell is not restrained in any way and can rotate in a vertical direction. An excellent treatment of shell stresses for penstocks supported on saddles is given by L. R Zick.3 Secondary stresses in a penstock shell near edges or corners of concrete anchors are not readily calculated. Some indication of the magnitude of these stresses may be realized by the use of finite element analyses. However, these stresses can be reduced by covering the penstock at these points, prior to concrete placement, with a tapering plastic material such as tar paper or cork sheeting. (3) Buckling due to axial compression Stresses caused by direct buckling or wrinkling failure of a thin shell occur whenever the shell is subjected to axial compression. Axial compression may be caused by bending action, temperature expansion in a longitudinally restrained penstock, by forces developed due to resistance against sliding, and by the compressive force developed by the weight of an inclined penstock with bottom anchorage. A treatment for determining the allowable, average buckling stress in a thin shell, considering the effects of imperfections due to fabrication, is given by L. H. Donnell and C. C. Wan. 4 Their analysis shows that the safe compressive stress that can be imposed on a steel cylinder shell without failure by wrinkling is one-twelfth the theoretical critical stress. Similarly, experimental tests show that the safe compressive stress that can be carried without buckling failure by wrinkling is given by: Sallow= ( )/3 1.5(106)ftj Sallow = 1.8(106)I(t< 0 rrI yieldpoint (for generalbuckling) 1/2yieldpoint (for local buckling) 78 (Equation4-9) (Equation4-10) 4 Exposed Penstocks Where: S&i.ow t r = = = allowable compressive stress, psi nominal shell thickness, in. inside penstock radius, in. A more refined treatment of penstock buckling under pressure is given by E.H. Baker, L. Kovalevsky, and F.L. Rish.5 (4) Longitudinal strain/stress Radial expansion due to internal pressure on an axially restrained shell will cause longitudinal contraction (Poisson's effect) with a corresponding longitudinal tensile stress equal to: SoP = PISM Where: So, t Si1 = = = (Equation4-11) longitudinal stress from Poisson's effect, psi Poisson's ratio (0.303 for steel) hoop stress due to internal pressure, psi This stress occurs only if the pipe is axially restrained. This stress should be combined algebraically with other longitudinal stresses calculated for the condition causing the Poisson strain/stress effect. (5) Temperature stresses The conditions under which thermal stresses occur can be distinguished in two ways: (a) The temperature and shell conditions are such that there would be no stresses due to temperature except for the constraint from external forces and/or restraints. In this case, the stresses are calculated by determining the shape and dimensions the shell body would take if unrestrained and then finding the forces required to bring it back to its restrained shape and dimension. Having determined these "restoring" forces, the stresses in the shell are calculated using applicable formulas. (b) The form of the body and thermal conditions are such that stresses are produced in the absence of external constraints, solely because of the incompatibility of the natural expansions and contractions of the different parts of the body. Where the position of ring girder footings, valve flanges, and other external attachments have to be fixed, thermal stresses and resulting displacements are important when the penstock is empty and when setting the penstock in place. Temperature differentials should be determined for the installation during both its construction and its operation. In addition, the position of the sun should be considered when determining thermal stresses L7, 79 Ca 4 Exposed Penstocks and displacements, and the resultant stresses and displacements should be resolved into components for use in design. If a thin-walled shell of a given length with both ends fixed is subjected to an outside temperature (T) on one side and an outside temperature (T+ AT) on the opposite side, and the temperature gradient between the two sides is assumed to be linear, then the fixed-end moments (MT) that develop at the end of the shell are given by: MT = (Equation4-12) Ey I AT cc D and the maximum resulting bending stress (Sm) is given by: C SMy AT jD Ey AT a (Equation 4-13) Where: Mr STB = = Ey AT D aX = = = = fixed-end moments maximum resulting bending stress Young's modulus for steel, lb/in. 2 differential temperature or change in temperature, °F nominal penstock diameter, in. temperature coefficient of expansion, in./in./F M = any moment C I = = distance to the most extreme fiber of shell subject to bending, in. moment of inertia of a section, in.4 If the thermal conditions described above are applied to a shell with both ends free, the shell normally would curve in the plane of the sun's rays at an arc of a circle having an inside radius (RI) of: D AT a Where: 00 0 radius of curvature of shell at its centerline, in. Rt = D AT cc = nominal penstock diameter, in. = differential temperature or change in temperature, OF = temperature coefficient of expansion, in./in./F 80 (Equation 4-14) 4 Exposed Penstocks The deflection (Y)at any point on the shell parallel to the plane of the sun's rays, as determined by a line drawn perpendicular to the original axis of the shell from the point to the longitudinal tangent drawn from the fixed end of the shell, is given by: AT cc L? (Equation 4-15) 2D Where: Y = AT = centerline deflection at any point of the shell, with one end fixed, due to differential temperature, in. differential temperature or change in temperature, 'F L = length, in. D = nominal shell diameter, in. Ifthe supports are permitted to rotate in a horizontal plane but about a vertical axis, then the angle of rotation (0) in radians is: AT =AL 2D (Equation4-16) Additional thermal stresses develop in a long, thin shell because of differential temperature conditions between the inside and outside surfaces of the shell. Assuming that the temperature gradient across the shell thickness is linear and that the outside temperature is higher, then the maximum circumferential stress at points remote from the ends of the shell is: - AT a Ey Sc- 2(l1-ti) (Equation 4-17) Where: SCT = = circumferential shell stress intensity due to differential temperature between inside and outside of shell, psi Poisson's ratio (0.303 for steel) Under the same conditions, the maximum longitudinal stress (in psi) is: AT ot Ey 2 SLr-- (Equation4-18) Both of the above stresses are compression on the outside and tension on the inside of the shell. At the ends of the shell, iffree, the maximum tensile stress is about 25% greater than the value given by the above equations. LU 81 ) 4 Exposed Penstocks If no restraint is imposed at the ends of a penstock, the load imposed due to temperature will be the resistance to sliding between shell and support and the resistance to sliding between shell and connecting joint (expansion or coupling). This latter resistance may be taken as 500 pounds per diameter inch. 4.1.3 Loading Combinations Given the above potentially active stress conditions, the designer should take into consideration probable combinations of loadings that may result in higher principal stresses. The stresses considered under normal conditions are: (1) Between supports (a) Longitudinal stresses due to beam bending (b) Longitudinal stresses due to longitudinal movement under temperature changes and internal pressure (c) Circumferential (hoop) stress due to internal pressure (d) Equivalent stress based on the Hencky-von Mises theory of failure or the stress intensities approach. (2) At supports (a) Circumferential stresses in the supporting ring girder or saddle due to bending, and direct stresses and tensile stress due to internal pressure (b) Longitudinal stress in the shell at the supports due to beam action and longitudinal movement from temperature changes and internal pressure (c) Bending stresses in the shell imposed by the support (ring girder or saddle) (d) Equivalent stress based on the Hencky-von Mises theory of failure or the stress intensities approach. Also, it may be important to consider the shear stress, as this may occur at or near supports and throughout the shell structure. It is important to keep in mind the secondary tension and compression stresses that can occur at an element of the shell and how the resulting Hencky-von Mises stress or stress intensities may govern design when these secondary stresses are combined with the primary hoop tension and beam bending longitudinal stresses. 4.1.4 Tolerances Penstock material plate or prefabricated pipe should be ordered with a thickness equal to or greater than the minimum thickness for handling or the thickness calculated for design. No additional adjustment needs to be made to the shell thickness if the specified mill tolerance will 082 4 Exposed Penstocks provide a plate thickness not less than the smaller of 0.01 in. or 6% of the nominalthickness. If greater tolerances are allowed, the design plate thickness should be increased to account for the undertolerance. Tolerances for steel plates and/or shapes are given by ASTM A20 and ASTM A6. Also, for an acceptable design thickness of the shell plate without any upward adjustment, it is important to apply minimum/maximum acceptance tolerances for shop and field weldment alignments at weld joints. The requirements of the ASME Code, Section VIII, Division 1 should be specified. 4.2 Ring Girders Ring girders normally are used to support long-span exposed steel penstocks. The purpose of the ring girder is to support the exposed penstock, its contents, and all live and dead loads as defined in Section 3.2. Also, ring girders stiffen the penstock shell and maintain the pipe section's roundness, thus allowing the penstock to be self-supporting, acting as either a simple or continuous beam when the penstock is supported by more than two supports. Ring girders allow the penstock to span relatively long distances (100 feet or more) compared to saddle-type supports (40 feet or less). Figure 4-1 shows a typical ring girder supporting a large-diameter penstock. See Section 3.4 for further definitions of types of stresses to be considered for ring girders. 4.2.1 Analysis Detailed ring girder stress analysis includes combining circumferential and longitudinal stresses in the penstock shell at the ring girder junction in accordance with Section 3.4. Added to the longitudinal beam stresses are longitudinal stress due to pressure on the exposed pipe end at the expansion joint, longitudinal stress due to frictional force at the supports, longitudinal stress due to frictional force at expansion joints or sleeve-type couplings, longitudinal force due to gravity (if the penstock is sloping), and localized bending stress in the shell due to ring restraint. The penstock shell away from the supports is also designed for combined longitudinal and circumferential stresses using the same procedure; however, bending stress from localized ring restraint is neglected. For exposed penstocks, it is common to thicken the shell in the vicinity of the ring girder. A detailed analysis method for ring girders has been published by the U.S. Bureau of Reclamation. 6 Also, an abbreviated version has been published. 7 83 4 Exposed Penstocks Brccing Olow rill 71- PLAN - RING GIRDER o -Oustside // OT rng SECT I ON rQd i us g rder 1 Figure4-la Typical Ring GirderSupportinga Large-DiameterPenstock 0 84 4 Exposed Penstocks Diaphragm pI 45 - alpart \ Ring girder !-H or i zonTa I ring pi -/ // 1 Typ Typ 1/4 114 Penstock IVerical I/4 I/4V \ --Verti l pipe shell ring pi LProvide drain holes in cOplhrogm DIates ctove The horizontal centerline SECT I ON Figure 4-lb Typical Ring GirderSupporting a Large-DiameterPenstock 4.2.1.1 Vertical Loads The basic procedure for ring girder design is to first locate the supports and then determine the reaction at the supports, assuming that the penstock acts as a continuous beam. A trial ring geometry is selected and the centerline of the support legs located such that the column centerline is approximately collinear with the centroid of the ring plus shell section. To minimize the ring bending moment, the centerline of the support legs should be located approximately O.04r inches outside the centroid of the ring plus shell section. The shell length (L1) that is assumed to be effective on either side of the ring is given by: L1 = 0.784'j- (Equation 4-19) Where: r t = inside radius of the shell, in. = shell thickness, in. For ring girders that use more than one ring, the maximum shell length (L2) that is assumed to be effective between the rings must not exceed 1.56-Frt. 8U 85 ( 4 Exposed Penstocks Next, section properties for the ring and the portion of the penstock shell that will participate in composite action with the ring are determined. Then the maximum ring and shell stresses for the vertical loads are calculated by combining the direct stress, bending stress, and pressure stress. Both the inside shell stress and outside ring tip stress then are compared with allowable stresses as defined in Section 3.4. The ring geometry is revised and the above analysis is repeated until stresses are acceptable. 4.2.1.2 Lateral Loads Ring girders also must support lateral forces due to wind or seismic conditions. Lateral forces should be evaluated according to Sections 1.7 and 1.8. The equivalent static lateral force must be not less than 15% of the vertical load. Horizontal seismic loading of ring girders produces a maximum bending at the horizontal springline of the penstock (where the support legs are attached to the ring). Vertical load stresses are combined with the seismic load stresses, and the area near the support leg attachments should be investigated to determine the stress magnitude and maximum stress location. The stresses then are compared with the allowable stresses defined in Section 4.2.4 to determine ifthe ring girder is adequate. Ifnot, the ring geometry is revised and the above analysis is repeated until stresses are acceptable. Also, stresses must be checked that occur in ring girders when the conduit is half full. These stresses are compared with the material and allowable stresses indicated in Section 3.4. The ring geometry must be revised until the stresses are acceptable. 4.2.2 Rocker Bearings Rocker bearings provide low resistance to longitudinal forces acting on the penstock support as the result of temperature changes, pressure, and gravity loads on inclined penstocks. Figure 4-2 shows a typical rocker bearing detail. The pin is designed as a beam with loadings introduced through the rocker and the side brackets. The following AISC formula (J8-2)8 establishes the basic rocker dimensions: F= -_13 Where: Fp = allowable bearing, kips/in. d = diameter of rocker, in. Fy = specified minimum yield stress of the steel, psi 86 (Equation4-20) 4 Exposed Penstocks I - -- - ag 9ir-der J -0jK~ 1 2__ Al 4 R E/ 22pi TLV) TO I SECTcker 3/ 3/4 ELEVATION 2-6" SECTION Figure 4-2 Rocker Bearing Detail Low resistance to friction can also be obtained by using slide bearings made of virgin Teflon®, high-density polyethylene (HDPE), or other products manufactured for the purpose of supporting heavy loads. These materials can reduce the coefficient of friction to 0.05 or less. Figure 4-3 shows a typical slide bearing detail that uses Teflon® bearing material. The upper surface of the bearing should be slightly larger than the lower surface to prevent debris from contaminating the contact surface of the bearing. LU 87 4 Exposed Penstocks Ring girder ver-tical supOrl" leg 0 0\0 0 v-ConcreTe Dier "-,ut ,rne o0 'oDDer eflon Dearing pad -,Outl ;ne of lower Teflon bearing pad 0 drain hole each end 0 00 0 ' Flat bar stops all around Bolts with nuts Base plate leveling PLAN n_ • !at car stop -iicrourcl I I S i I I- ass :late ill with non-snrink grout after level ing ana sel-ting ring girder N-~ in place level ring nuts Concreie pier Boairts WTh Figure 4-3 Ring GirderSlide Bearing 4.3 Saddles Saddles are a type of support for exposed penstocks. The support engages less than the full perimeter of the penstock, generally between 90 and 180 degrees of arc, and typically 120 degrees. Saddles are simpler to construct than full-perimeter ring girder supports, but generally are spaced closer together than ring girders. The closer spacing is necessary because saddles do not stiffen the penstock shell against radial deformations to the same extent as ring girder supports. Saddles, serving the same functions as ring girders, act as supports to carry water and penstock metal loads or as construction supports. They may be of steel or reinforced concrete. Figure 4-4 illustrates several typical saddle configurations. 088 4 Exposed Penstocks 1800 > 6 > 60 ApprOx. Wear-\ 200 _____ p aaI e- r ola~e \,s iffeners r. eeper _L5 ase Il-fe t Grout r S I idi Dear i n eg Weare pla (A) STEEL SADDLE I wear-.e-n p late 180 > 8 > 1200 e ie n . Rebar S li ngsheets. coran Tea . SECTION (B) CONCRETE SADDLE -Saddle WFol 1ec e shades Braces - -Oase , rate SECTION -' (C) TEMPORARY STEEL (ConstrucT ion) Figure4-4 Saddle Configurations 4.3.1 Wear Plates Wear plates sometimes are used between the saddle and penstock shell to stiffen the shell and limit local stresses in the shell immediately around the saddle plate. Wear plates can serve as the interface between the penstock and saddle that allows differential expansion to take place. To be effective in reducing shell stresses, wear plates must extend beyond the saddle plate they bear upon by an amount in the longitudinal direction of about 16 wear plate thicknesses plus the differential growth, and in the circumferential direction by about 6 degrees of arc. Wear plates are attached to the penstock shell by a continuous fillet weld. Corners of the wear plate are cut with a radius to reduce stress concentrations. LU 89 ) 4 Exposed Penstocks 4.3.2 Stiffener Rings Full-circumference stiffener rings can be used on either side of the saddle to stiffen the penstock shell or can be placed in the same cross section as the saddle itself and made integral with the saddle. Stiffener rings make possible span lengths approaching those permitted by ring girder supports. 4.3.3 Steel Saddles Steel saddles generally are fabricated from structural grades of steel (A36 is the most common) and are of welded construction. Wear plates and stiffener rings, which stiffen the penstock shell directly over the saddle, generally are welded to the penstock; therefore, these items must be of the same material as the penstock shell or of a compatible material with the same nominal chemical and mechanical strength as the penstock shell material. Also, the items must be heat treated to similar notch toughness as the shell, and have good weldability to the penstock. See Section 2.4 for specific material requirements for saddles, wear plates, and stiffener rings. 4.3.4 Expansion Provisions Saddles may be designed to act as anchors to resist pressure forces at bends in the penstock and also loads directed along the length of the penstock. The loads acting along the length of the penstock are from friction forces generated at supports as a penstock expands or contracts due to temperature changes or pressure surges, and from the axial component of gravity loads on inclined penstocks. If not fixed, saddles generally are designed to permit sliding, relative to the penstock, either at the saddle-to-penstock interface or at the base of the saddle. Ifsliding is at the base of the saddle, keeper bars are required to prevent the penstock from moving in the transverse direction. 4.3.5 Stability Saddle design requires a stability check to ensure that the saddle will not overturn when acted upon by lateral forces in directions along the penstock axis or transverse to the axis. Generally, no uplift or point of zero bearing is permitted anywhere on bearing surfaces with a factor of safety against overturning of at least 1.5 for Design Basic Criteria (DBC) earthquake and 1.0 for the Dam Safety Criteria (DSC) earthquake. Stability considerations require that the minimum bearing on the right support shown in Figure 4-5 satisfies the expression: W -Hhd Where: W H 090 L(h, R+ b'('I"2' = total reaction normal to centerline, kips = total transverse load, kips 0.0 (Equation 4-21) 4 Exposed Penstocks L = total longitudinal load, kips = 3 for DBC and 2 for DSC e (The distances R, b, h, c, and d given in Figure 4-5 must be in consistent units of length.) I -W Figure4-5 Saddle Stability Diagram Longitudinal load (L) and transverse load (H) often are due to frictional forces caused by penstock expansion, in which case they become proportional to reaction (W), where the proportionality factor is the friction factor. Friction factors for design are given in Reference 7. For saddles that are not welded to the penstock, stability considerations require that the following expressions be satisfied: Where: H W 0 tan-1 (Hlw)• 0. 125(0) for DBC (Equation4-22) tan-1 (H/w)• 0.25(0) for DSC (Equation4-23) = total transverse load, kips = total reaction normal to centerline, kips = total contact angle between saddle and penstock, degrees These expressions ensure contact between the penstock and saddle over at least 3/4 of the arc subtended by the full saddle angle (0) for the Design Basis Criteria (DBC) earthquake, and 1/2 the saddle angle for the Dam Safety Criteria (DSC) earthquake. The expressions assume that longitudinal force (L) is uniformly distributed along the saddle arc and does not affect transverse stability. 91 Ql) 4 Exposed Penstocks 4.3.6 Saddle Design 4.3.6.1 Shell Stresses Figures 4-6 and 4-7 show the shell stresses that must be considered in saddle design. Saddle contact angle 6 = =1 Neutral axis R = Mid-surface radius t = Thickness I = Moment of inertia 2 3 t(A+ sinA cosA-2 sin top - Section modulus, Za Zb = Section modulus, 0= b sinA -cos A R( L sin A - bottoom = (A) SECTION MODULUS OVER SADDLE (Stiffener rings not used) e Saddle contact angle V 1 1-40 Shear at support 19 r mox 180° - a (B) = 'rmax = VK2 K2 =ýor- a1 s n a sin a cos TANGENTIAL SHEAR STRESSES AT SADDLE (Stiffener rings not used) a W W = Total reaction, kips WK5 = Compression force, kips K = (HT- a)I + + Cosa sina cose 5 Longitudinal length of shell resisting compression force = 1.5 4f + D ( wi thout wear plate) or = 1.56 plate of width g) WK5 JWI + g (with wear Compressive stress = 1.56 WK5 or = , or ( 1.56 R +-t gI) + gt WK 5 • 2 t2 = thickness of wear plate (C) CIRCUMFERENT IAL COMPRESSION SHELL OVER INVERT OF SADDLE IN (Stiffener rings not used) Figure4-6 Saddle Design Shell Stresses 092 + b)t 4 Exposed Penstocks FIXED-ENDED ARCH ms = Bending moment at 0 ( in.-Ibsl 8 = Saddle contact angle (roaa nsl W = Total load/reaction P• M.p maximum at 0 = 9 M0 ,,. [os 0+± sin r.~-1 ,510 Cos MO Thrust P0 ,cs [9- 4-o1 (+c - 7222 =cs3 2~ I-2 n 2 load, Po, aIt 0 =9 E_ [ 0 sin A COA] os 9 ]+ 7• 2(1 - CO'sg) cos 9 )( R( I - Cos/3(/ Mt Where Mt= Mo when 0 = 0° Width of shell resisting P0 is 1. 561t + b b = Width of saddle or wear plate, in. t = Penstock thickness, in. R = Penstock radius, in. Width of shell resisting Mp equals the lesser of 8R or center-to-center span length of saddle supports. Example: If span length 2< 6MA BR, then horn bending = 6MO and total thrust plus bending = -•2 For a wear plate of width g (g>b) total stress P0 ( 1 and thickness t 2 , 1 = (1.56 FR-t + g) t + gt i 6MO 2 + t 22 i Figure 4-7 CircumferentialStress at the Horn of a Saddle (Without Stiffener Rings) The Zick approach 9 for the analysis of shell stresses is an accepted method. The Zick method determines the shell stresses (items 1 to 5) or forces and moments in the saddle or ring stiffeners (items 6 and 7) as follows: (1) Beam bending stresses over the saddle support and at midspan At midspan the full circumferential section modulus (7uR 2t) is available to resist bending. R is the mid-surface radius, and t is the penstock wall thickness. Both maximum compression and maximum tension must be checked. Maximum compression usually occurs with all loads acting and pressure at its minimum value. The allowable compressive stress must be limited to the allowable specified in the ASME Code, Section VIII, Division 1, UG-23(b), for axial compression in a thin-walled cylinder. Alternatively, rules in API 62010 9U3 93 D 4 Exposed Penstocks may be used. As specified in API 620, for values of LiR less than 0.00667, the compression stress (in psi) must not exceed 1.8xl 06 (t/R). (See also Section 4.1.2.3 (3).) Over the saddle, the bending stress is assumed to be resisted by an arc of shell less than the full circumference (for saddle supports that do not utilize stiffener rings). The effective shell arc for resisting longitudinal beam bending over the saddle equals twice the angle delta (A) (see Figure 4-6(A)). Ifstiffener rings are used to stiffen the penstock at saddle supports, the full cross section may be used. (2) Tangential shear stress at the horn of the saddle The horn of the saddle is the edge defined by the angle 0 shown in Figure 4-4. Beam shears at the saddle are assumed to be resisted by tangential shear stresses lying in the midsurface of the shell and acting over an arc of shell slightly larger than the saddle contact angle. In Figure 4-6(B), the angle (xdefines the effective arc for resisting shear; the shear stresses vary in magnitude with the sine of the angle measured from the vertical centerline. (3) Circumferential compression stress directly over the invert of the saddle See Figure 4-6(C) for the method of checking the circumferential compression stress in the penstock directly over the invert of the saddle. (4) Circumferential stress at the horn of the saddle The circumferential stress at the horn of the saddle is a combination of PL + Q stresses; the stress limit is held to 1.5KS by Zick.9 Circumferential bending and thrust forces are assumed to have the same values as would result for a fixed-ended circular arch as shown in Figure 4-7. The calculated bending moments are distributed over a fairly long length of shell to give results consistent with strain gage testing. Generally, pressure stresses are not combined with stresses from the calculated bending and thrust stresses because pressurizing the penstock stiffens and rounds it out. (5) Additional head stress Additional head stress generally is not applicable to long conduits supported on multiple supports, such as a penstock. (6) Stiffener ring forces and moments If stiffener rings are used over or adjacent to the saddle, they must be designed for the circumferential bending moments, shears, and thrust loads resulting from the loading. A conservative method for calculating these forces and moments is shown in Figure 4-8 (when stiffener rings are adjacent to the saddle) and Figure 4-7 (when the stiffener ring is in the same plane as the saddle web). 094 4 Exposed Penstocks (a) Ring st iffener integral with saddle (lies in same plane as saddle web plate). Use bending moments and thrusts developed in Figure 4-7. (b) Ring stiffeners adjacent to saddle (stiffeners lie outside pIane of saddle web plate). Use bending moments and thrusts as follows; R = Radius To centroid of stiffener-shell composite section W = Total reaction. kiDs = Saddle angle (degrees) Angles in formulas are in radians. For trigonometric functions, angles con be either in degrees or radians. 2cos( BENDING MOMENT: WRý) F(7 ) snp 27T Lsiný -2i® Mbmaximum ate t -8 co?[3 c s (7_ [ Z / o - ) o A 7 THRUST: W 7T Where _ 0 s I n Csn / S-€ •2( I• LTC--co -cos Mt = Ms when 5 e= 7 -+zr) Cos P I -Cos ~R( Ri-ca ý)CSp+, 0' Figure 4-8 Saddle Design - Stiffener Rings Adjacent to Saddle (7) Saddle forces A tension force in the saddle is needed to balance forces from the assumed cosine distribution of pressures applied radially to the saddle at the contact between saddle and penstock. Refer to Section 4.3.6.3 and Figure 4-9. The horn circumferential bending stress plus direct stress generally governs selection of the saddle contact angle and may govern shell thickness. For the circumferential check of stresses, it is assumed the penstock is not under pressure. It is assumed the penstock rounds out when pressure is applied, thereby reducing the bending stress over the horn of the saddle. It is necessary to check only the horn circumferential stress with internal pressure at zero. 4.3.6.2 Analytical Method The Zick method9 is recognized as good practice. However, today's broad use of computers and the availability of software tools for the finite element method of analysis give very good results if applied by experienced designers. These analytical methods are accepted for checking shell stresses near the saddle proper. LU 95 CA1 4 Exposed Penstocks 4.3.6.3 Design and Analysis of Saddles Design of the saddle itself should follow good structural engineering practice. For steel saddles, requirements specified in the AISC "Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings"11 must be met. Figure 4-9 provides formulas for bending moment, shear, and thrust in the design of the saddle proper. Concrete saddles should meet ACI 318 building code12 requirements for concrete. Load distribution on the saddle as shown in Figure 4-9 is theoretically correct and is used for design. W A = Area ( in. sector 2 ) of circular subtended 2 r = Pseudo unit 12q by angle 1P ) (e-s in 0 8-= wi. Jnt Ioading ( I s/in.) cos(8 /2 )] Y = 2 ( lbs./in. ) rcos = (W/A o- R = Radius of saddle. Angles in formulas are in radians. For trigonometric functions, angles can be eiTher in degrees or radians. (A) DISTRIBUTION ON SADDLE DUE TO LOAD W UIF Ve = - - A Incnes R-2(cos 4> - cos 0/2 ) (sin 8/2-sino 2 R 2 A2 812 R( case - cos 8/2) in -E [(0/2 - 40 - sin 2 A, and A2 ore areas (6/2 - o )] (in. 2 ) U = Y (A, +A2 )( lIbs.) --= -- - cos 8/2 )2 U and V are horizontal vertical load resultants pt. P. Point P (B) ( cos 0 RESULTANT FREE-BODY FORCES AT POINT P (Act through center as shown) Free-body diagram angle A to angle Resolving forces U and V about Horizontal Shear. Bending Note: force, U = Y(A1 moment, Saddle reaction V = -y-- 8/2 point P (coso- gives: cos 0/2)2( Ibs. ) + A 2 )( lbs. ) M,= R(V cos 4>- to balance U sino )( in.- load W is lbs. ) assumed to be at o Figure4-9 Forces and Moments for Design of Saddle Proper lb 096 hi and at =0 4 Exposed Penstocks 4.3.7 Detailing Various configurations have been used successfully in penstock construction. Details illustrated in Figure 4-4 are typical of those used and should not be construed as the only acceptable details. The sliding surface at the base of the steel saddle shown in Figure 4-4 (A) also could be located at the saddle plate/wear plate interface. In that case, the sliding bearing at the base of the saddle would not be necessary, and the base of the saddle would be anchored to the foundation with anchor bolts. The saddle plate of the saddle proper shown for the steel saddle in Figure 4-4 (A) and (B) should be formed at a radius that accounts for the theoretical radius of the penstock when the penstock is under design pressure. According to Zick,9 the saddle width at the interface with the penstock does not control proportioning the design. A minimum saddle width (dimension a in Figure 4-5) of 12 inches for steel saddles and 15 inches for concrete saddles is recommended. 4.4 Stiffeners 4.4.1 Circumferential Stiffening Full circumferential stiffener rings should be provided on exposed penstocks when required to resist external pressure such as vacuum. 4.4.2 Stiffener Spacing To determine spacing of stiffener rings and required shell thickness, the procedure in UG-28 of the ASME Code, Section VIII, Division 1 must be followed. 4.4.3 Moment of Inertia Requirements The size of stiffener rings must meet the moment of inertia requirements of UG-29 of the ASME Code. Alternatively, the moment of inertia (I) of intermediate stiffener rings must satisfy the formula?: pLDWO (Equation4-24) 77,300,000(N2_1) Where: I p = moment of inertia of the composite stiffener ring and participating part of the penstock shell (the shell length must not exceed 1.1 (Do)"), in. = external pressure, psi LU 97 CO 4 Exposed Penstocks L D, N 2 = stiffener spacing, in. = outside diameter, in. = number of complete waves into which a circular ring will buckle 0.663 < 100 N (ID;) (/DD½• 0 H = distance between ring girder supports or end stiffeners, in. t = penstock shell thickness, in. 4.4.4 Welding Welds attaching stiffener rings to the penstock must be in accordance with UG-30 of the ASME Code, Section VIII, Division 1, which gives acceptable sections and structural shapes for use as stiffener rings and methods of attachment. Stiffener ring splices should be full-fusion butt joints designed to develop the full section of the stiffener ring. 4.4.5 Tolerances on Roundness The roundness tolerances specified in UG-80 of the ASME Code must be met. 4.4.6 Line-of-Support Line-of-support for purposes of determining stiffener spacing may be a cone-cylinder junction, provided the moment-of-inertia of the junction meets the rules for stiffener rings specified in UG-29 of the ASME Code. Ring girder supports are often adequate to serve also as stiffeners to resist external pressure but must meet Section 4.4.3 moment-of-inertia requirements. 4.4.7 Factor of Safety Although the ASME Code rules are based on a theoretical factor of safety of 3 for external pressure, the tolerances were established to limit the buckling pressure to not less than 80% of that for a perfectly circular vessel. Implicitly, the true factor of safety is 3 x 0.8 = 2.4. This factor of safety is not considered overly conservative for exposed penstocks constructed to normal fabrication tolerances. A factor of safety of 3 is used in the moment of inertia equation for stiffener rings in Section 4.4.3. 4.4.8 Attachment of Stiffener Rings Fillet-welded attachment of stiffener rings is permitted. The maximum size of fillet welds used to attach stiffener rings to a penstock made of heat-treated material, such as ASTM A517, which is quenched and tempered, should be limited to 3/8 inch and the welds must be continuous. Stitch welding is not recommended for any material. With the exception of stitch welding, the rules specified in UG-30 of the ASME Code are recommended. (I) 0 98 4 Exposed Penstocks 4.5 Bends Changes in direction of flow are accomplished with curved pipe sections commonly called bends. Bends up to 24 inches in diameter may be smooth, wrought, or steel fittings, as specified in Section 2.4 or fabricated from mitered sections of pipe. Bends greater than 24 inches in diameter commonly are fabricated from mitered sections of pipe. The mitered pipe sections must be joined by full-penetration, single- or double-welded butt joints. 4.5.1 Fabrication The radius of bends must be equal to or greater than 1 pipe diameter but need not be greater than 3 pipe diameters. Special situations, such as a bend immediately upstream of a turbine or a free discharge valve, may warrant larger radius bends. Bends may be fabricated by mitering segments of a cone to produce a reducing bend or by mitering straight pipe segments to produce a constant diameter bend. An analytical stress investigation as recommended in Section 4.5.3 should be undertaken. The maximum deflection angle of the mitered segment must not exceed 22.5 degrees. Other methods that consider discontinuity stresses may be used. 4.5.2 Compound Bends Compound bends are required where it is desired to change flow direction in both plan view and profile. Trigonometric calculations are necessary to determine the true angle of the bend and end rotations.7 4.5.3 Stress Analysis Bends with a radius less than 2.5 pipe diameters must be designed with consideration given to concentration of hoop tension stresses along the inside edge of the bend. The following formula 13 is used to check stresses: PD(tD 0+S t= - -- tan-+ 2 2) Sf (ý3 Where: t (Equation4-25) = required elbow wall thickness, in. P = design pressure, psi f = allowable tensile stress at design pressure, psi D = outside diameter of elbow, in. S 0 = segment length along inside of elbow, in. = segment deflection angle, degrees Stresses calculated according to this formula must not exceed the limits specified in Section 3 for P,,. To satisfy the formula, short radius bends may require thicker plate than adjacent sections of straight pipe. 9U 99 U 4 Exposed Penstocks 4.6 Welded Joints 4.6.1 Types and Configurations Typical welded joint configurations for longitudinal and circumferential main welded joints are shown in Figure 4-10. (A) FULL-PENETRATION BUTT JOINT (•7 Butt (B) FILLET-WELDED BUTT STRAP (Circumferential welded butt strap) B•-8ackup 2" xl/4" (C) oar min. SINGLE-WELDED, FULL-PENETRATION BACKED-UP BUTT JOINT ' (D) [ 4t DOUBLE FULL-FILLET LAP JOINT Figure 4-10 Welded Joint Configurations(I) 0 /T yp 10) 100 4 Exposed Penstocks Configurations for nozzle and manway penetrations, attachments, and corner joints are shown in Figure 4-11. Stiffener.7 3Z Ins ide penstock (A) / ring ) Inside Nozzl1e neck (Note I pensIocR I NOZZLE WITH PAD REINFORCING Nozz• (D) ATTACHMENT e neck L iner wall '/s 3 Stud /AItr ]Insert /f late---nate Inside-penstock (B) (Note (E) I NOZZLE WITH BUTT-WELD INSERT REINFORCING (Not to stud weld STUD-WELDED ATTACHMENT recommended for nignmater ials with yield strengths 75 _ksi). strength Notes: I Examine surfaces b~y YAT before FlIat plIate -(Note 2) >a+b) > 2t a-Ž t or'1/4 (Note 3) (C) t Cylinder and after welding to detect presence of laminar tearing. 2. Examine weld prep and edge "c by MT before welding. Repair defects. After welding examine by MT weld surface one edge "c" agoin. FULL-PENETRATION CORNER JOINT 3. The (a+b) _2t rule nelps prevent laminar tearing. Figure4-11 Welded Joint Configurations(ll) Lu 101 ct 4 Exposed Penstocks Configurations for bifurcation joints are shown in Figure 4-12. PP Web --7 F l ange Reinforcemenrib Shell-/ FuH I penerrotion Weld overlay UT and weld reQair ail IlminaTions I DETAIL F' P 1 DETAIL PP 2 SECT I ON A- Figure4-12 Welded Joints-Bifurcations Detail 1 of Figure 4-12 shows an acceptable detail at the junction of a bifurcation shell (or skin) to the center reinforcing girder. Other details have been successfully used; however, the one shown is a good illustration of such a joint. Special precautions are necessary to avoid or minimize susceptibility to lamellar tearing. These special precautions include: use of weld overlay and ultrasonic examination before and after welding; use of material conforming to low sulfur practice; manufacture of the material by forging (to ultrasonic-tested quality); and the requirement that the material meet specific tensile properties in the three orthogonal directions c102 4 Exposed Penstocks (e.g., specific through thickness properties of elongation, impact energy, and tensile strength). The joints between the bifurcation shell and center reinforcement are full-fusion, full-penetration welds, and are 100% examined either ultrasonically or by radiography and also by the magnetic-particle method. 4.6.2 Butt Joints Welded joints required to be examined by radiography and ultrasound must be full-penetration butt welds. 4.6.3 Double-Welded Lap Joints Double full-fillet lap joints must be limited to thicknesses not greater than 3/8 inch for longitudinal joints and 5/8 inch for circumferential joints. 4.6.4 Joint Qualifications Prequalified welded joints for complete penetration groove welds that meet the AISC 4 Specification for Structural Steel Buildings1 and the AWS Structural Welding Code (D1 .1-92)15 are acceptable for penstock construction. 4.6.5 Pipe Welds Circumferential joints in pipe 24NPS and smaller in diameter may be joined by full-penetration, single-welded groove butt welds without backing strips. 4.6.6 Bolted Joints Bolted flanged joints meeting ANSI B16.5 requirements are acceptable for joints in pipe 24NPS and smaller in diameter. Bolted joints that meet the ASME Code, Section VIII, Division 1 requirements are acceptable for all diameters of penstocks. 4.6.7 Single-Welded Lap Joints Single-fillet, welded lap joints are acceptable for circumferential joints in penstocks 24NPS and smaller in diameter provided the joint is prequalified and the thickness does not exceed 3/8 inch. 4.6.8 Backed-Up Butt Joints For a number of reasons, backed-up joints generally are not used if joints are required to undergo radiographic or ultrasonic examination. First, it is difficult to interpret radiographic or ultrasonic indications that invariably show up on the film (RT) or scope (UT). Second, if access for installing film to the backed-up side is available, welder access also usually is available and it is preferable to double weld the joint. Backed-up joints for circumferential joints are common for water pipes and carbon steel penstocks where radiography or ultrasound is not required and L0A 103 l 4 Exposed Penstocks thicknesses are 11/4 inches or less. For quenched and tempered high-strength material, such as A517, backed-up joints should not be used. Ifbacked-up joints have the back-up bar removed at the completion of welding and are examined by RT or UT, they are acceptable if a prequalified detail. 4.6.9 Back-Up Bar Splices Where backed-up joints are permitted, splices in the back-up bar must be full-penetration butt welds. 4.6.10 Grout Connections Figure 4-13 shows a weld detail for a welded grout connection with a pad. C4112' ýb o' M i n. , Note 4 0 S /gap Ins id ( Note I)I/ N I"" E3 0 9 E/ line 1M31/2" Steel plug 2"cp straight "X 8 threads provided with or nubin for (Note 2) holes, slot, tightening; seal with Teflon® tape or O-ring • g x i/8" type stainless 304 seal plate ,Note 3) Notes: ( I) Before welding. (2) Maximum diameter that does nOT require 100% rep I acement. 13) Stainless for ductility and corrosion/erosion resistance (I/8" thicrs to minimize projection into waterway). (4) Chamfer corners To prevent bonding to concrete, (5) Minimum tnicKness Y/4" for threac engagement. Figure4-13 Grout Connection - Weld Detail Figure 4-14 shows a grout connection without a pad (see Figure 4-13 for details not shown). 2 104 4 Exposed Penstocks 2'"q straight thread 1I lug L 2%,Max. ~1 " n-- for I/-• f rounc groove 0-ring sea I Figure 4-14 Grout Connection Without Pad 4.7 Transitions 4.7.1 Geometric Transitions 4.7.1.1 Diameter Changes Changes in diameter are usually accomplished by the use of right conical shells placed in the straight tangent portion of a line or combined with a mitered bend as shown in Figure 4-15. Cone angles, diameter ratios, and miter angles shown in these sketches are recommended but not mandatory. At angle changes in the profile of the penstock (cone-cylinder or miter-to-miter) greater than those recommended, special discontinuity analysis is necessary. One method for this analysis is given in the ASME Code, Section VIII, Division 1, Appendix 1-5. Stiffener rings sometimes are required at these junctions. Geometric layout of mitered conical sections bends is given in AWWA Manual M11 .16 LU 105 C 4 Exposed Penstocks RIGHT CONICAL MITERED (A) REDUCING BEND 2 .5•! R/D •10 F Iow Fiow direction HL (B) RIGHT CONICAL REDUCER (INLINE) 9 < 50 L>!4 (C) RIGHT CONICAL REDUCER (Aligned invert shown 0 for effective to 70 (D-d) (OFFSET) drc inage) !5 50 to 7° a • 70 L ->4(D-d) Figure4-15 Typical Geometric Transitions Figure 4-16 illustrates a change in diameter effected by a contoured transition of parabolic form. Such transitions are often used at inlets to the penstock and at the inlet/outlet of surge tanks. 0106 4 Exposed Penstocks 1 ~-Transition Figure 4-16 ContouredChange in Diameter 4.7.1.2 Cross-Section Shape Changes Figure 4-17 illustrates a square-to-circular transition. The transition is made up of flat triangular sides and oblique conical quarter sections at the four corners. Such shapes cannot resist the pressure of water forces with membrane type stresses only and, therefore, must be stiffened. Moment resisting frames can be used for stiffening. Each frame must be continuous around the perimeter and spaced to limit bending stresses in the flat plate liner between stiffeners. Ifthe transition is embedded in structural reinforced concrete or mass concrete, anchor studs welded to the exterior side of the transition can be used in place of stiffener frames. D, (1 Di, -c Obl iQue cone Note: D, 5 2. 2) D •-Stiffener/seeogce rings one D2 need not be equa 1. Figure 4-17 Square-to-CircularTransition Other geometric forms can be used for geometric transitions provided the form can contain pressure with essentially membrane forces only. The form must be stiffened if it cannot contain pressure with essentially membrane forces only. The ASME Code, Section VIII, Division 1, Appendix 13 contains rules for the design of noncircular cross-section conduits, both stiffened and unstiffened. LU 107 4 Exposed Penstocks 4.7.2 Thickness Transitions 4.7.2.1 Tapers A tapered transition having a length not less than three times the offset between the adjacent surfaces of abutting sections, as shown in Figure 4-18, must be provided at butt joints between sections that differ in thickness by more than one-fourth of the thickness of the thinner section, or by more than 1/8 inch, whichever is less. The transition may be formed by any process that will provide a uniform taper. When the transition is formed by removing material from the thicker section, the minimum thickness of that section, after the material is removed, must be not less than that required to resist pressure (such as hoop stress). When the transition is formed by adding additional weld metal beyond what would otherwise be the edge of the weld, such additional weld metal buildup must undergo examination by MT or PT and be included in the examination for the butt weld. The butt weld may be partly or entirely in the tapered section or adjacent to it. z min. FenstocK- inside of DensTock Figure 4-18 Change-in-Thickness Transition(Butt Weld) 4.7.2.2 Nozzle/Branch to Penstock Transitions A transition between a forged nozzle or branch and the penstock is illustrated in Figure 4-19. Note the detailing feature of using a radius at the otherwise sharp corner to keep stress concentrations to reasonable levels. For some materials, details utilizing fillets and chamfers at sharp comers are sufficient. Generally, the ASME Code details, which reflect good practice, should be used. Figure 4-19 also illustrates a transition from the thick nozzle neck to a thinner branch pipe. In this case a steeper taper of 1:1 is shown but a radius is used at the end of the taper where it meets the thinner pipe. 0108 fl' 4 Exposed Penstocks r-cncn NozzIe neck -NI NC zi Inside ofpenstock i ! Figure4-19 Contoured Transition 4.7.2.3 Other Transitions in Thickness The ASME Code specifies other types of transitions in thickness, in joint misalignment, at changes in direction (such as at a mitered joint), at flanges, and at contouring of forged fittings. The ASME Code limitations and requirements apply to any transition not specifically covered in this manual. 4.7.3 Material Transitions Figure 4-20 indicates an acceptable transition in material, where the transition is made up of a spool piece of higher strength material (material 2). Material Inside I-- 3 min., •• I /-Mater i al 2 of L > 2. 0 FRt, penstock Matericl Matericl I: 2: Lower-strength material Hiaher-strergtrh material t2 > tI Figure4-20 Typical Change in MaterialTransition LU 109 4 Exposed Penstocks References* 1. Roark, R.J. and Young, W.C. Formulasfor Stress and Strain. McGraw-Hill Book Co., New York, NY (1975). 2. Schorer, H. "Design of Large Pipelines." Transactions.ASCE. 98:101 (1933). 3. Zick, L.P. "Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports." Welding Journal(Welding Research Supplement). 30:435-S (Sept. 1951). 4. Donnell, L.H. and Wan, C.C. "Effects of Imperfections on Buckling of Thin Cylinders and Columns Under Axial Compression." Journalof Applied Mechanics (1950). 5. Baker, E.H., Kovalesky, L. and Rish, F.L. StructuralAnalysisof Shells. McGraw-Hill Book Co., New York, NY (1972). 6. "Penstock Analysis and Stiffener Ring Design." Bulletin No. 5, Part 5. Boulder Canyon Project Final Design Report. U.S. Bureau of Reclamation, Denver, CO. 7. Bier, P.J. "Welded Steel Penstocks-Design and Construction." Engineering Monograph No. 3. U.S. Bureau of Reclamation, Denver, CO (1986). 8. Manual of Steel Construction, Allowable Stress Design. American Institute of Steel Construction, Chicago, IL (9th Ed., 1989). 9. Zick, L.P. "Useful Information on the Design of Plate Structures." Steel Plate Engineering Data-Volume 2. American Iron and Steel Institute and Steel Plate Fabricators Association, Inc. (Feb. 1979). 10. Recommended Rules for Design and Construction of Large, Welded, Low-Pressure Storage Tanks. API Standard 620. American Petroleum Institute, Washington, DC. 11. Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings. American Institute of Steel Construction, Inc., Chicago, IL(Nov. 1, 1978). 12. Building Code Requirements for Reinforced Concrete. (ACI 318). American Concrete Institute, Detroit, MI. 13. Standard for Dimensions for Fabricated Steel Water Pipe Fittings. ANSI/AWWA Standard C208-83(R89). AWWA, Denver, CO. 14. Specification for Structural Steel Buildings-Allowable Stress Design and Plastic Design, June 1, 1989. American Institute of Steel Construction, Inc., Chicago, IL. * The cn 7C)110 I most current version of a standard, code, or specification should be used for reference. 4 Exposed Penstocks 15. Structural Welding Code-Steel. ANSI/AWS D13.1-92. American Welding Society, Miami, FL. 16. Steel Pipe-A Guide for Design and Installation.AWWA Manual Ml 1. AWWA, Denver, CO (1989). The following references are not cited in the text. Parmakian, J. "Minimum Thickness for Handling Steel Pipe." Water Power & Dam Construction(June 1982). Pirok, J.N. "Some Problems of a Penstock Builder." ASCE Journalof the PowerDivision 83, (PO 3). Paper 1284 (June 1957). Seely, F.B. and Smith, J.O. Advanced Mechanics of Material.John Wiley & Sons, Inc. (2nd Ed., 1952). "Test of Cylindrical Shells." University of Illinois Bulletin No. 331. (Sept. 23, 1941). "Welded Steel Pipe." Steel Plate EngineeringData-Volume 3. American Iron and Steel Institute and Steel Plate Fabricators Association, Inc. (1989). Wilson, W.M. and Newmark, N.M. "The Strength of Thin Cylindrical Shells as Columns." University of Illinois EngineeringStation Bulletin No. 255 (Feb. 1933). Zick, L.P. and St. Germain, A.R. "Circumferential Stresses in Pressure Vessel Shells of Revolution." ASME (Sept. 1962). L11